System components such as mechanical couplings, sensors, and actuators often require precision for applications in which the performance of feedback control systems is critical. For instance, precise control of an electro-mechanical system such as a robot is important for many applications in industrial automation, consumer products, and logistics and supply chain operations. A common mechanical coupling in robotics utilizes gear couplings or gearboxes. Gearboxes can be particularly useful because electromagnetic transducers can deliver very low torques at very high speeds. In applications, such as robotics, where bidirectional actuation with a gear reduction, a hydraulic servo valve, or a piezoelectric transducer, for instance, is often necessary, backlash, dead-zone, and hysteresis can severely limit the performance of feedback control systems.
Backlash in a gearbox is the amount of space between mating components of gears. By design, this space is built in to account for, inter alia, imprecision in gear manufacture and thermal expansion. In applications in which the gear couplings can be reversed, such as robotics, backlash of the mating components of the gears negatively affects the ability of the gears to translate input motion into instantaneous output motion. Moreover, this hard non-linearity prevents accurate positioning and may lead to chattering and limit-cycle type instabilities. This increases the wear and tear on gears, which, in turn, further increases backlash.
Dead-zone is a type of non-linearity in which the system does not respond with an output until the input reaches a certain level. Sometimes this type of non-linearity is intentional. For instance, systems may incorporate a small dead-zone to prevent constant operation and thus reduce wear and tear around a nominal operating point. Dead-zone is distinct from backlash and hysteresis in the sense that it does not have memory of previous operating conditions.
Backlash is a form of mechanical hysteresis due to space between mating components in a transmission, i.e., the “play” between parts. More generally, hysteresis indicates a state dependency on the history of the state of the system. An example of a system that demonstrates hysteresis is a spring that undergoes both elastic and plastic deformation. When compressed, due to the plastic deformation, the rest position of the spring will change depending on how far the spring was compressed. Thus, the state of the spring (rest position) depends on the history of the system.
In standard gear trains, backlash is inevitable due to the over-constrained nature of gears. Care can be taken to significantly reduce backlash by tight tolerancing, but at significant cost. Other solutions to backlash have been developed. In one approach, harmonic drive gearboxes have zero backlash, but suffer from high flexibility, resonance vibration, friction and structural damping nonlinearities, and are typically proprietary and expensive. In another approach, cycloidal gearboxes are another style of gearbox which remove backlash, and while they do not share the same durability issues as harmonic drives, they still tend to be proprietary and expensive.
In another approach, anti-backlash gears are used. In application, an anti-backlash gear mates with a standard gear. A typical arrangement consists of two concentric gears, with one gear rigidly held to the shaft and the other gear coupled through a spring with a set pre-tension. The gear teeth of both anti-backlash gears sandwich the standard gear, and depending on the direction of force, independently act as the load path of the gear train. Thus, as long as the pre-tension is not overcome, the anti-backlash gear effectively captures and tracks the previous gear in the gear train, and there is no backlash. When the pre-load is overcome, however, the position of the anti-backlash gear becomes a function of the loading, the spring constant, and the pre-load, which has been viewed as an undesirable behavior.
In still another approach, dual actuators are used. In a typical configuration, two or more drives are utilized in parallel connection to the final output stage. Backlash is reduced by small positional differences in the drive, effectively replicating the effect of anti-backlash gears. Active control and synchronization is generally required between the drives, however, to manage positional differences and prevent large undesirable torques.
Some applications can tolerate a compliant drive, and may—as in the case of series elastic actuators—even require it. A typical approach in such applications is to find a gearbox with an appropriate level of backlash and an independent compliant system, and combine them. Although the gearboxes are chosen based on their relationship between input motion and output motion, the whole system behaves with an input motion and an output force or torque.
Furthermore, techniques exist for computationally addressing system non-linearities such as backlash, hysteresis, and dead-zones. These approaches include implementing inverses of the non-linearities in the controllers or implementing adaptive, fuzzy, or neural network control techniques. However, in most cases the parameters of the non-linearities are unknown, and more generally, these techniques can be complicated and may not provide robust performance over a wide range of plant or environmental conditions.
What is needed, then, is a system for reducing or minimizing backlash, hysteresis, and dead-zones that is uncomplicated, cost-effective, and durable.